DIGing and ATC tracking, as well as another gradient tracking algorithm Aug-DGM, have an explicit state variable \(^k\)  to track the global gradient, which is the reason we call them explicit gradient tracking algorithms.
Besides these explicit gradient tracking algorithms, there also exist lots of other distributed algorithms, like EXTRA, NIDS, Exact diffusion, and so forth. Though they do not possess the explicit gradient tracking structure, we found that they do have an implicit one, hence they can also be seen as gradient tracking algorithms, but with the implicit tracking approach. The implicit tracking mechanism (approach) is first proposed in [1]}, which is employed to develop efficient algorithms for distributed constraint-coupled optimization problems. Specifically speaking, [1]} offers a new perspective to understand a classical continuous-time distributed optimization algorithm [3]}, which is given as
 
 = -f() – ,
